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Introduction

Whenever sliding mechanics are used in ortho-dontics, friction generated between the bracketand the archwire has a major impact on the forcedelivered to the teeth (Frank and Nikolai, 1980).

Friction is defined as the resistance to motionwhich is called into play, when it is attempted toslide one surface over another with which it is

in contact (Tweeny and Hughes, 1961). A distinc-tion is made between static frictional force definedas the smallest force needed to start a motion ofsolid surfaces with respect to each other, andkinetic frictional force defined as the forceneeded to resist the sliding motion of one solidobject over another at a constant speed. Slidingfrictional force is the component of total contactforce between the surfaces which is in the direc-tion of intended or actual sliding motion and

opposing this motion. The other componentsof the contact force are perpendicular to thefrictional component and are referred to asnormal force.

Since continuous arch mechanics comprise anoverwhelming part of orthodontic treatments,friction influencing the rate and type of toothmovement has attracted considerable interest,resulting in a large number of experiments

designed with the purpose of analysing thevarious aspects of friction. Materials, size andshape of brackets and wires, and type of ligationhave been analysed in wet and dry conditions,and at room and mouth temperatures. The influ-ence of the materials comprises two factors, thealloy and the surface structure of both bracketsand wire. With regard to the magnitude of thecontact surface most authors agree that frictionincreases with increasing wire dimension and

European Journal of Orthodontics 20 (1998) 283291 1998 European Orthodontic Society

Frictional forces related to self-ligating brackets

Luca Pizzoni*, Gert Ravnholt** and Birte Melsen***

*School of Orthodontics, University of Milano, Italy, **Departments of Prosthetics and***Orthodontics, Royal Dental College, Aarhus University, Denmark

SUMMARY Orthodontic tooth movement can be regarded as teeth sliding on a wire like pearlson a string, the force being supplied by springs or elastics. The movement implies frictionbetween wire and bracket, taking up part of the force and leaving an uncontrolled amountto act on the teeth. The friction is likely to depend on bracket construction and wire material.Therefore, in this investigation the friction of self-ligating brackets and beta-titanium wireswas evaluated, as opposed to more conventional configurations.

Carried by low-friction linear ball bearings, a bracket was made to slide along an out-stretched archwire with minimal (and known) basic friction, either parallel or at an angle tothe wire. Two self-ligating brackets were used in their closed position without any normal

force. Friction was tested against four wires: stainless steel and beta-titanium, both in roundand rectangular cross-sections. The force used to overcome friction and to move the bracketwas measured on a testing machine at 10 mm/min, and the basic friction was subtracted.

The results show that round wires had a lower friction than rectangular wires, the beta-titanium wires had a markedly higher friction than stainless steel wires, and friction increasedwith angulation for all bracket/wire combinations. The self-ligating brackets had a markedlylower friction than conventional brackets at all angulations, and self-ligating brackets,closed by the capping of a conventional design, exhibited a significantly lower friction thanself-ligating brackets closed by a spring.

The selection of bracket design, wire material, and wire cross-section significantlyinfluences the forces acting in a continuous arch system.

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bracket width. It is likewise generally agreed thatfriction largely depends on surface roughness andcoefficient of friction of the involved materials(Angolkar et al., 1990; Kusy et al., 1991; Vaughanet al., 1995). In addition, a linear relationship

between the normal force delivered, when thewire is inserted into the bracket, and friction hasbeen demonstrated repeatedly. Lately Yamaguchiet al. (1996) focused on the influence of the pointof force application with respect to the centreof resistance and stressed, as earlier studies(Drescher et al., 1989; Tidy, 1980), the role thebiological resistance of the periodontium plays inrelation to friction.

Review of methods

Investigations on friction can be divided into fourmain groups according to the type of set-up used:

1. Archwires sliding through contact flats, limit-ing the studies to the influence of materialsonly (Kusy and Whitley, 1989; Stannard et al.,1986).

2. Archwires sliding through brackets parallelto bracket slot, allowing the analysis of theinfluence of material, bracket design and wiredimension in addition to impact of saliva and

different types of ligation (Garner et al., 1986;Baker et al., 1987; Angolkar et al., 1990;Berger, 1990; Kapila et al., 1990; Kusy andWhitley, 1990; Pratten et al., 1990; Kusy et al.,1991; Sims et al., 1993; Downing et al., 1994,1995; Saunders and Kusy, 1994; Shivapuja andBerger, 1994; Keith et al., 1994).

3. Archwires sliding through brackets with differ-ent second and third order angulations allowedthe study of the influence of the variation ininterbracket configuration (Andreasen and

Quevedo, 1970; Frank and Nikolai, 1980;Peterson et al., 1982; Prosoki et al., 1991; Simset al., 1994; Tselepis et al., 1994; De Francoet al., 1995).

4. Recently, study designs in which the bracketssubmitted to a force were allowed a certainfreedom of tipping resulting in a retarding ofthe applied force has attempted to simulatethe impact of the biological resistance to toothmovement (Tidy, 1980; Drescher et al., 1989;

Yamaguchi et al., 1996; Bednar et al., 1991;Ireland et al., 1991).

As the interaction between the involvedvariables clearly influences the results, it is

important to design any experiment on fric-tional forces with new brackets and materialsusing well characterized frictional forces usinga known material as a control.

The purpose of the present study was to applythe third type of design to four types of brackets,one well known self-ligating (Speed, SpeedSystem, Cambridge, Ontario, Canada), twoconventional brackets to which a standardnormal force was applied and one of the latterbrackets to which a self-ligating device was

added (the Damon SL bracket, Ormco, Glendora,CA, USA); to test these brackets against twoknown materials in two dimensions and at fivedifferent second order angulations.

Material and methods

The wires used for the test were stainless steeland beta titanium in two different dimensions,round 0.018 and rectangular 0.017 0.025 inches.The brackets were one Dentaurum (Dentaurum,Pforzheim, Germany) and two A-Company

(A-Company Europe, Amersfoort, The Nether-lands) conventional upper premolar bracketswithout torque. One of the A-Company brackets,the Damon SL bracket, had a specially designedcoverage so that the bracket became self-ligating(Figure 1). The last bracket included was theself-ligating Speed bracket to serve as a controlfor the newly designed Damon SL bracket. Allbrackets had the same vertical slot size (0.022inches). The horizontal dimension of the bracketvaried as seen in Table 1.

The experiments were carried out using aTensometer 10 testing machine (Monsanto plc,Swindon, UK) with a 25 N tension load cell anda chart recorder. The measuring device usedon the testing machine comprised an aluminiumcarriage with four smooth linear ball bearingsmade to run on two vertical, parallel rods ofpolished, hardened steel (Figures 2 and 3). Alonga third rod, parallel to the first two, an archwirewas suspended, parallel to the motion of the

284 L . P IZ Z ON I E T A L.

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carriage; the wire was fixed at the lower end(where carriage motion starts) and kept under3 N tension by a spring at the upper end.

Each bracket was mounted with cyanoacrylateglue on the end of an acrylic rod with a diameterof 6 15 mm, which was fixed to the carriage,facing the archwire, and adjusted in two planesof space so the bracket slot would engage the

wire and slide along it with minimal friction(Figures 2 and 3).

The self-ligating brackets were used in theclosed position. Over the conventional bracketsa small brass tube with two 5-mm lengths of0.010 inches soft stainless steel wire resting at anangle of 90 degrees on the archwire was placedso that a normal force of 2 N perpendicular tothe base of the bracket was delivered to the arch-wire. This force was generated by a spring fixed

to the carriage. The first test was carried out withthe bracket slot parallel to the direction of dis-placement, while the bracket in the subsequentexperiments was rotated from this initial position(slot parallel to the wire) to a fixed angulation of3, 6, 9, and 12 degrees with respect to the wire.

The weight of the carriage was balanced bytwo symmetrically positioned counterweights

with strings and ball bearing pulleys, allowing thecarriage to be moved vertically with the leastpossible force. The measuring device framewas attached to the testing machine frame, andthe carriage was connected to the cross-head bya thin wire. Four archwires and four types ofbrackets and five different angulations resultedin a total of 80 combinations. Each combinationwas tested for 80 mm movement at 10 mm/mincross-head speed; two runs were made for each

FRICTIONAL FORCES AND SELF-LIGATION 285

Figure 1 The two self-ligating brackets. (a) The Damon SL bracket. (b) The Speed bracket.

(a) (b)

Table 1 Survey of the materials used.

Dentaurum A-Comp. A-Comp. Speed

Ligation conventional conventional self-ligating self-ligatingSlot size (inches) 0.022 0.030 0.022 0.028 0.022 0.028 0.022 0.025Slot length (inches) 0.145 0.125 0.120 0.089

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possible combination. The tests were made atroom temperature and in the dry state.

The validity of the measurements was estab-lished through the evaluation of the inherent fric-tion of the measuring device. This was calculated

as an average of 10 dry runs with no engagementbetween bracket and wire. These results servedas the generation of a correction factor by whichthe test results were adjusted.

The analogue output from the Tensometer 10testing machine was connected to an X-T recorderfor visual control of the measurement values,and to an analogue-digital converter and a PC forprecise data acquisition. The stick-slip nature offriction tended to yield values expressing spikesand glitches. To overcome this, an electronic low

pass filter was inserted in the analogue outputpath. The action of the filter was a short-termaveraging of signal, rendering data more readablewithout affecting the long term variation and theabsolute values.

The AD conversion was carried out with a10-bit resolution, dividing the measurement rangeinto 1024 steps. Sampling intervals were 250milliseconds, yielding a total of 1920 measure-ments sampled per run.

ResultsThe results illustrated in Figure 4ad representthe four different types of wire included in theexperiments. The variation within the individualcombination of the tests appears in Table 2. Itwas obvious that both alloy and wire dimensionhad a major impact on friction. As expectedTMA showed a considerably higher friction thanstainless steel at all angles and with all brackets.In addition, the wire dimension also affectedfrictional forces, but not always in a predictable

manner. Wire dimension and alloy exhibited aclear interaction with angulation.

Whereas a linear relationship between fric-tional forces and increasing angulation seemedto exist in the case of the conventional brackets,the self-ligated behaved differently. With a rect-angular wire the frictional forces observed withthe self-ligating brackets increased dramaticallywhen the angulation was 9 and 12 degrees. Theimpact of wire dimension and alloy was likewise


Figure 2 Schematic drawing of the experimental set-up.(a) Frontal view illustrating the possibilities for angulation.(b) Lateral view illustrating the sliding mechanics.

a b

Figure 3 Photographic illustration of the experimental set-up.

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highly dependent on the type of bracket. Gener-ally, the self-ligating brackets exhibited lessfriction than the conventional brackets. At noor small angulations and with round wires thesebrackets demonstrated a very low friction com-pared with the conventional brackets loaded witha normal force. At larger angulations betweenthe brackets and the wire the Speed bracketexhibited a significantly greater increase in fric-tion than the other brackets. Among the conven-tional brackets the Dentaurum bracket exerted

less friction than the A-Company bracket of thesame dimension.

The dependency of the frictional forces onthe angulation was noteworthy, indicating thatthe increase in frictional forces with increasingangulation was more pronounced in the case ofstainless steel than TMA wires. The dimensionlikewise played a more important role in the caseof stainless steel than in the case of TMA wires.Apart from the combination of zero degree

angulation and rectangular wire where the Speedbracket exhibited higher friction, probably relatedto its smaller horizontal dimension and the specialspring design, both the self-ligating brackets weresuperior than the conventional brackets. TheDamon SL bracket from A-Company exhibitedeven less friction than the Speed bracket withrespect to all wire types (Figure 4ad).

Discussion

In the selection of orthodontic materials athorough knowledge of their physical propertiesis crucial. New materials should therefore besubmitted to testing, allowing for comparisonwith known materials. In the present study a newself-ligating bracket and three known bracketswere tested against two materials, two wiredimensions and five different angulations. It wasconfirmed, as previously demonstrated (Angolkaret al., 1980; Tidy 1980; Drescher et al., 1989;


Figure 4 (ad) Bar charts showing the results of the different combinations. Note that the scale of they-axis varies betweenthe graphs.

c

a b

d

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Kapila et al., 1990; Kusy and Whitley, 1990a,b;Kusy et al., 1991; Downing et al., 1994) that TMAexhibited an unacceptably high friction whichwas only to a limited degree dependent on thedimension. The friction was clearly related to thesurface structure of TMA and has recently led

to surface treatment with ion beam implantationreducing the friction significantly (Kusy et al.,1992). The dependence on angulation was morepronounced in the case of stainless steel thanTMA, a possible reason being the lower stiffnessof the latter wire. The importance of wire stiff-ness as a factor affecting frictional forces(Nikolai and Frank, 1980) was confirmed inour experiment, where stiffer wires exhibitedincreased friction at all angulations probably due

to the normal force which increases at the contactpoint. In the case of the Damon SL bracket nonormal force was present at zero angulation andthe binding which started at 6 degrees was mostpronounced with rectangular wires, leading to arapid increase in friction with respect to all wires.

Within the same type of bracket, except in thecase of the Speed bracket, friction with roundwires exhibited higher dependency of angulationthan friction with rectangular wires. The lowfriction related to the self-ligating bracketreflected the lack of normal force in the case ofthese brackets. As the wire was undersize and nofriction could be anticipated in the experimentswithout angulation, consequently only insignifi-cant obstruction to a free movement could be


Table 2 Frictional forces expressed as mean and SD (below) for each combination.

Bracket Wire 0 3 6 9 12

Dentaurum 0.018 0.769 0.968 1.269 1.617 1.985

convent. SS 0.048 0.052 0.056 0.068 0.082Dentaurum 0.017 0.025 1.107 1.333 1.716 2.139 2.591convent. SS 0.054 0.052 0.142 0.163 0.152Dentaurum 0.018 2.462 3.445 3.396 4.598 6.395convent. TMA 0.298 0.406 0.446 0.440 0.534Dentaurum 0.017 0.025 2.255 3.052 3.272 3.786 4.602convent. TMA 0.564 0.544 0.288 0.368 0.578A-Comp. 0.018 1.441 1.494 1.742 2.440 2.775convent. SS 0.070 0.152 0.130 0.239 0.185A-Comp. 0.017 0.025 1.471 1.501 2.050 2.601 3.137convent. SS 0.106 0.162 0.156 0.198 0.223A-Comp. 0.018 3.712 4.342 6.220 7.670 7.880convent. TMA 0.728 0.724 1.048 0.934 0.994A-Comp. 0.017 0.025 3.678 4.002 4.444 5.016 7.706convent. TMA 0.415 0.336 0.314 0.378 0.736

Damon 0.018 0.156 0.413 0.782 1.250 1.718A-Comp. SS 0.025 0.030 0.044 0.050 0.079Damon 0.017 0.025 0.130 0.119 0.656 1.188 1.749A-Comp. SS 0.021 0.033 0.043 0.062 0.088Damon 0.018 0.111 0.700 1.529 3.325 5.664A-Comp. TMA 0.021 0.104 0.227 0.394 0.626Damon 0.017 0.025 0.116 1.252 3.387 5.464 8.398A-Comp. TMA 0.029 0.163 0.388 0.594 0.996Speed 0.018 0.152 0.278 0.704 1.207 2.009

SS 0.026 0.031 0.044 0.044 0.082Speed 0.017 0.025 1.002 0.975 1.431 2.371 3.278

SS 0.081 0.074 0.123 0.107 0.168Speed 0.018 0.173 0.273 1.025 2.432 5.006

TMA 0.025 0.062 0.100 0.272 0.384Speed 0.017 0.025 3.208 3.952 4.682 7.866 12.711

TMA 0.398 0.326 0.486 0.748 0.705

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verified in the case of the Damon SL bracket.For the Speed bracket, the spring coveragecould account for the friction related to thisbracket at zero angulation as the spring deliversa normal force depending on the dimension of

the bracket. While Berger (1990) found Speedbrackets to generate a significantly lower frictionthan conventional brackets at wire dimensionsup to 0.016 0.022 inches, Sims et al. (1993)reported higher frictional forces with increasingwire dimensions up to 0.019 0.025 inches. Thesefindings suggest that friction in relation to Speedbrackets could possibly be related to the slotdepth and spring tension rather than archwirewidth. This conclusion is consistent with thediscrepancy between the extremely low friction

related to round wires and high friction relatedto rectangular wires found in this study. The effectof the flexible coverage depends on the presenceand absence of contact between wire and spring,and thus is dependent on the surface structure ofthe wire and the force delivered by the spring.This also may explain the perceived need for thedevelopment of a special wire cross-section. Inthe case of the Damon SL bracket no normalforce is delivered as the bracket is transformedinto a tube 0.022 0.028 inches when closed. Thisaccounts for the negligible friction at zero degree

found in this study and that for the ActivaBracket in previous studies (Sims et al., 1993,1994). The dependence on angulation, independ-ent of bracket type stresses the need for align-ment before sliding mechanics are used (Tidy,1980; Drescher et al., 1989; Sims et al., 1994). Thecomparison between the Damon SL bracket andthe conventional A-Company bracket is note-worthy as the brackets are identical apart fromthe method of ligation. This makes it possible tofocus on the influence from the normal force

which is often high even at zero angulation.In the present study only the presence or

absence of a normal force was evaluated, how-ever, the type of ligation may also be important(Frank and Nikolai, 1980; Peterson et al., 1982;Stannard et al., 1986; Kusy and Whitley, 1990;Bednar et al., 1991; Shivapuja and Berger, 1994)and an interaction between ligation with elasto-mers and the width of the brackets may con-tribute to the explanation of the diverging results

on bracket width and friction (Kapila et al.,1990). Another factor of importance may be thespringiness of the wire, which would explainthe difference in behaviour. In our experimentthe normal force was always kept at 2 N, in the

clinical situation the friction would increase evenfurther, where ligation of rotated teeth maygenerate a higher normal force and elastomersmay generate both a higher and a lower forcedepending on the stretching of the elastics.

Conclusions

The present study confirmed that friction is aproduct of factors that may interact in variousways. The mechanism of these interactions may

explain the often conflicting results reported bydifferent authors. The importance of the surfacestructure was clearly confirmed as the TMA gaverise to significantly more friction than stainlesssteel. Both stiffness and springback of the wirewas of importance when the bracket was slidingalong a wire at a certain angle. The stiffer thewire and the lower the springback, the higherthe friction generated. The spring design of theSpeed bracket resulted in significant frictioneven at small angles between brackets and wire.The wire dimension also exerted a significant

influence. In the case of an undersize round wirethe Speed and the Damon self-ligating bracketsresulted in significantly less friction than anyof the conventional brackets. In the case ofrectangular wires the Damon bracket wassignificantly better than any of the otherbrackets and should be preferred if slidingmechanics is the technique of choice.

Address for correspondence

Birte MelsenDepartment of OrthodonticsRoyal Dental CollegeAarhus UniversityVennelyst Boulevard8000 Aarhus CDenmark


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Acknowledgements

This study was supported by A-Company,Amersfoort, The Netherlands.

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